Smooth Fano polytopes arising from finite directed graphs
Combinatorics
2015-11-04 v4 Algebraic Geometry
Abstract
In this paper, we consider terminal reflexive polytopes arising from finite directed graphs and study the problem of deciding which directed graphs yield smooth Fano polytopes. We show that any centrally symmetric or pseudo-symmetric smooth Fano polytopes can be obtained from directed graphs. Moreover, by using directed graphs, we provide new examples of smooth Fano polytopes whose corresponding varieties admit K\"ahler--Einstein metrics.
Keywords
Cite
@article{arxiv.1103.2202,
title = {Smooth Fano polytopes arising from finite directed graphs},
author = {Akihiro Higashitani},
journal= {arXiv preprint arXiv:1103.2202},
year = {2015}
}
Comments
13 pages, 4 figures